A geographic information system (GIS) that performs computerized analysis of map/image data/information to support decision making processes was developed in the 1960s. A historical treatment of this subject is given by Roger F. Tomlinson entitled, “Geographic Information Systems—A New Frontier,” The Professional Geographer, 1984, pp. 31–35; reprinted in Introductory Readings in Geographic Information Systems, edited by Peuquet and Marble, pp. 18–29. From the beginning, spatial information such as map data was collected from a paradigm deep-rooted in classical geometry that views the world in terms of three shape primitives: 1) point, 2) line, and 3) polygon, and their corresponding topological relationships as shown in FIGS. 1 and 2, extracted from “A Classification of Software Components Commonly Used in Geographic Information Systems”, Design and Implementation of Computer-based Geographic Information System, edited by Peuquet and O'Collanghan, Amhurst, N.Y. IGU Commission on Geographic Data Sensing and Processing, pp. 70–91.
Point, line and polygon are based on “measured x,y locations” for locational data. A point has one (x,y) data point, and a line has multiple data points in which two points are connected to form a straight line segment. A a polygon is a closed, 2-D shape enclosing a space by a boundary contour which is made of multiple straight line segments.
As shown in FIG. 2, a conventional GIS spatial model, and topological relationships are structured according to these spatial primitives:                1) node is a point that has an (x,y) coordinate;        2) link is a straight line segment that connects two nodes;        3) link has an identification (ID);        4) polygon is composed of multiple closed links;        5) polygon has an ID; and        6) link has a right polygon and a left polygon.        
Since this model is inherent in the Environmental Systems Research Institute's (ESRI) ARC/Info, the most popular GIS software, it is clear that a point/line/polygon-based spatial structure is still the dominant GIS paradigm.
In the early 1990s, the term “topological relations” was extended from the aforementioned classic geometry paradigm to a two-object spatial relationships model in the framework of algebraic topology, as evidenced in “A Framework for the Definition of Topological Relationships and an Algebraic Approach to Spatial Reasoning Within This Framework”, by Egenhofer, Herring Smith, and Park, Technical Paper 91-7, NCGIA, September 1991. This algebraic topology-based spatial model is similar to the classical point/line/polygon model. For example, in “The 9-Intersection Formalism and Its Use for Natural-Language Spatial Predicates”, (Technical Report 94-1, NCGIA, May 1994), Egenhofer and Herring wrote:
“The algebraic-topology spatial data model is based on primitive geometric objects, called cells, which are defined for different spatial dimensions: a 0-cell is a node (the minimal 0-dimensional object); a 1-cell is the link between two distinct 0-cells; and a 2-cell is the area described by closed sequences of three non-intersecting 1-cells. A face of an n-cell A is any (0 . . . n) cell that is contained in A.”
From the above basic definition, cells for regions, lines, and points are defined as follows:
A region is a 2-complex in R2 with a non-empty, connected interior.
A line is a sequence of connected 1 complexes in R2 such that they neither cross each other nor form closed loops.
A point is a single 0-cell in R2.
In this point/line/region framework, spatial relationships are developed by intersecting two shape primitives in numerous possible conditions. For example, the authors showed 33 relations between two simple lines as shown in FIG. 3.
“Topological Relations in the World of Minimum Bounding Rectangles: A Study with R-tree”, by Papadias, Theodoridis, Sellis and Egenhofer (Technical Report 94-8, NCGIA, December, 1994) illustrated some relationships between two regions as: 1) disjoint (p,q), 2) meet (p,q), 3) overlap (p,q), 4) Covered by (p,q), 5) inside (p,q), and 6) equal (p,q) as shown in FIG. 4.
If the classical geometry-based point/line/polygon structure is denoted as Model #1 spatial topology, and the above-discussed disjoint/meet/overlap/etc configuration as Model #2 spatial topology, Model #1 conceptualizes points, lines and polygons existing on the same plane. Consider a commonly-known house plan as an analogy. Model #1 restricts points, lines, and polygons on the same floor.
Model #2 conceptualizes the existence of objects in terms of a multiple-plane architecture. For example:
Scenario #1: a same plane structure to accommodate:                1) disjoint (p,g), and (2) meet (p,q)        
Scenario #2: multiple planes structure to accommodate:                3) overlap (p,g), (4) covered by (p,q), (5) inside (p,q), (6) equal (p,q) and so on.        
By using the same house floor structure for illustration, for condition (3):                Object p exists on the first floor of the house, and        Object q exists on the second floor of the same house.        
This multi-layer spatial structure is necessary to accommodate the Scenario #2 condition. Basically, in a real world GIS system, it requires that a space or entity on the surface of the Earth is occupied by one object for one particular application or coverage. Otherwise, there exists a topological conflict or there is no topological integrity.
Using this axiom, the classical geometry-based point/line/polygon structure illustrated in FIG. 2, the conditions of disjoint (p,q) and meet (p,q) illustrated in FIG. 4 do not have a topological integrity problem; whereas, overlap (p,q), covered by (p,q), inside (p,q), and equal (p,q) have a topological integrity problem as summarized in Table 1.
TABLE 1Spatial Relationships in The Context of Topological IntegrityModel #1 ConditionsModel #2 Conditions(1) Relationships without Topological(2) Relationships with TopologicalProblem, But has Limited CapabilityConflicts, But has Much MoreIn Object RecognitionCapability in Object Recognitionpoint, line. Polygon structureoverlap, covered_by,In FIG. 2Inside, equal, etcDisjoint, meet in FIG. 4In FIG. 4
As noted in Table 1, both Model #1 and Model #2 conditions have certain weaknesses and strengths in handling spatial data/information for constructing a GIS for object recognition.
It would be advantageous to provide an object recognition system to accommodate both Model #1 and Model #2 conditions in such a way that objects can be extracted and recognized in an environment where constraints on topological integrity are not required, and at the same time, the corresponding scene structure/object can be displayed and outputted to an environment with full topological integrity.
It would also be advantageous to provide a data processing environment in which an object can be differentiated by its ID in both segmentation cycle and input layer, thus allowing objects to exist in a non-topology-integrity-compliance environment.
It would also be advantageous to provide a means for objects extracted in a non-topology-integrity-compliant environment to exist in an environment constrained for topological integrity.
In addition, it would be advantageous to provide a means by which objects with full topological integrity can be generated automatically from image data without having to manually digitize and edit the node, the line, the polygon, etc.
Furthermore, it would be advantageous to provide a means to visualize and edit, if necessary, the object and/or its corresponding boundary/chain/node and attribute table.
It would also be advantageous to provide a means to compute and display discrepancies between two sets of boundary contours—an observed and a standard—for change detection and accuracy assessment under a full topological integrity paradigm after they are extracted under a feature/object extraction system in which topological integrity is not an issue.
It would be extremely advantageous to provide a means to recycle again and again a set of extracted objects back into the system in a multi-layer structure to extract additional objects and features for which information processing is done by words and concepts (i.e., multiple facets of the characteristics of an object, the combination of which is difficult to quantify precisely) instead of crisp numerical analysis.
It would be even more advantageous to provide a means to automatically generate a word and concept based rule set that requires the user only to point and click the locations where the target object and its associated features are located (i.e., verbal articulation of how the target object is to be extracted is not required).